NEW YORK -- The last time the New York Yankees and Boston Red Sox got together on July 1, Aaron Hicks hit three homers and David Price was roughed up. It added up to an 11-1 rout for the Yankees and both teams exited Yankee Stadium tied for first place in the American League East.

It seemed the dogfight for AL East supremacy was on, but the Red Sox gradually pulled away. When the rivals get together Tuesday afternoon for the opener of a three-game series, they will have differing goals.

The Red Sox (103-47) will clinch their third straight AL East if they win one game in the series. When they clinch, it will be their fourth in seven seasons since the Yankees last won the AL East in 2012.

The Yankees (91-58) will try to prevent the Red Sox from celebrating at Yankee Stadium for the second time in three seasons while attempting to keep their lead in the wild-card race.

The reason for the differing goals is because of what unfolded for the teams after their last meeting in New York. It was the last time the Yankees and Red Sox were tied for the lead. Since then, Boston is 47-18 and New York is 37-31.

"That would be awesome," Red Sox ace Chris Sale told reporters in Boston after Sunday's 4-3 win over the New York Mets at Fenway Park put them on the verge of clinching. "I think we'd all like to do it here, obviously, but we weren't able to do that.

"Going to one of your biggest rivals in the division or in the game and being able to do it there, it will be fun. We'll enjoy it anywhere we're at."

The Yankees hold a 1 1/2-game lead over the Oakland A's and can feel fortunate to still have home-field advantage. While the A's dropped two straight, so did the Yankees, losing two one-run games to the Toronto Blue Jays to continue a stretch of inconsistent performances in the last three weeks.

The Yankees are 8-11 in their last 19 games since a 5-3 win on Aug. 29 in Baltimore. That capped a 15-5 run immediately after the Red Sox completed a four-game sweep in Boston over the Yankees to take a 9 1/2-game lead.

"First of all, it's never too late. We're not even close to too late," Yankees manager Aaron Boone said after Dellin Betances allowed two runs and four hits in the eighth inning on Sunday. "We've got to play better, clearly. We're not playing our best right now. But the history of this game is littered with stories of teams that went into the playoffs in different scenarios: limping, playing great.

"The bottom line is, you've got to be playing right when it counts, and don't mistake that for 'This is OK,' but I still believe at my core that we have everyone in that room to do something special."

The Yankees have been getting healthier in recent weeks with the return of Gary Sanchez (groin) and Didi Gregorius (heel). It's possible that Aaron Judge (fractured right wrist) could return to the lineup Tuesday and closer Aroldis Chapman (left knee) could also return at some point in the next few days.

The Yankees activated Judge on Friday since there are 40-man rosters, but all he has done was play two innings in right field Friday.

Without being able to pencil Judge into the starting lineup since he was hit by Kansas City right-hander Jakob Junis, the Yankees are 26-22, including 14-12 at home. During those games, the Yankees are batting .234 (365-for-1,562).

"Every team goes through it," Judge said. "Right now, you don't want to go through it, especially when it's late like this, but we've still got plenty of baseball left to get hot.

"It's all about what team is hot. If we can get hot here in the last two weeks and take that into the playoffs, we're going to be in a good position."

Mookie Betts will likely play for the Red Sox on Tuesday and be the starting designated hitter. He injured his left side making a throw and exited Sunday's game as a precaution.

"You know, I was just coming out of it for precautionary (reasons), just to make sure it didn't get any worse," Betts said. "But it checked out to be just fine."

Former Yankees pitcher Nathan Eovaldi gets the start for the Red Sox. He is 2-3 with a 4.17 ERA since being acquired from Tampa Bay just before the non-waiver trade deadline.

Eovaldi last pitched a week ago as a reliever when he allowed two runs in 3 2/3 innings of a 7-2 win over Toronto. He faced the Yankees on Aug. 4 and allowed three hits in eight scoreless innings of a 4-1 win.

J.A. Happ, who missed the series in Fenway because of hand, foot and mouth disease, starts for the Yankees. He is 6-0 with a 2.70 ERA in eight starts for New York.

Happ remained unbeaten as a Yankee when he allowed six hits in six scoreless innings during a 7-2 win on Sept. 10 at Minnesota.

The veteran left-hander is 7-4 with a 2.98 ERA in 19 career appearances against Boston.

Boston leads the season series 8-5. The rivals close out the regular season next weekend with a three-game series at Fenway.